High School Physics Friction

So, we know about forces, multi-dimensional kinematics, and Newton’s 3 laws of motion; now it’s time to add some real-world aspects to our problems. Friction is a way of objects trying to stay put and not move. Friction can be thought of as an anti-force; it tries to keep objects from moving and stop objects in motion. Since friction is a force, unless otherwise stated, it should be included in your free-body diagrams from now on, and factor into any calculation of which it is relevant. Next time we’ll finish our force discussion in mechanics.

Hey Professor,I just wanted to let you know that your doing a great job, but is it normal to have a hard time solving the problems, because I understand the theory part but when it comes to application I have been having a hard time, so can you give me some tips on how to improve my capacity in Physics through the application point of view. Thanking you,Dinesh

1 answer

Last reply by: Professor Selhorst-JonesWed Apr 1, 2020 10:14 AM

Post by beihur777on April 1 at 12:11:32 AM

Is the normal force always equal to the force of gravity. Let's say that there is a block that is being acted on by a force upward. Would the normal force be equal to the force of gravity minus the upward force, or would it just be equal to the force of gravity?

1 answer

Last reply by: Professor Selhorst-JonesMon May 15, 2017 11:32 PM

Post by sania sarwaron April 26, 2017

which geometry lesson would you recommend in order to understand example 2's math?

1 answer

Last reply by: Professor Selhorst-JonesFri Mar 25, 2016 6:25 PM

Post by Peter Keon March 7, 2016

At 49:29, why F_fric=m_2*a and not F_fric=u_s*m_2*g?

1 answer

Last reply by: Professor Selhorst-JonesMon Oct 6, 2014 11:59 AM

Post by Tori Carrollon October 5, 2014

I have a question on a problem similar to your third example. Say a box of mass m is held at rest against a vertical wall by a horizontal force FA. The wall has coefficient of friction Î¼. How would you solve for the minimum coefficient of friction Î¼ in terms of FA, m, and g?

1 answer

Last reply by: Professor Selhorst-JonesSun Jul 28, 2013 9:01 PM

Post by enya zhon July 27, 2013

Which type of objects have greater static friction than kinetic friction? Just curious.:) Thanks!!!:):)

1 answer

Last reply by: Professor Selhorst-JonesSun Oct 28, 2012 9:49 PM

Post by varsha sharmaon October 28, 2012

in example 3 shouldn't it bemg-fric.= 0 ( because the object is moving down )(though by doing your way ,the answer will be the same)

3 answers

Last reply by: Professor Selhorst-JonesWed Oct 17, 2012 1:58 PM

Post by Nik Googoolion August 30, 2012

50/m.g=

50/98=0.51 not 0.71

1 answer

Last reply by: Professor Selhorst-JonesThu Sep 6, 2012 4:48 PM

Post by Patrick Gomezon August 7, 2012

I love Physics! It's amazing how a person's whole way of viewing the world around them changes as they continue to learn more.

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Friction

Friction changes depending on the two materials involved. Wood on rubber is different than wood on wood is different than wood on ice. (This idea is captured by our coefficient of friction: μ.)

Friction changes depending on how hard the two materials are pushed together. (This idea is captured by the normal force between the two materials: FN.)

Friction changes depending whether or not the two materials are already in motion relative to each other-static vs. kinetic. (This idea is captured by having two different coefficients of friction: μs and μk.)

Kinetic friction is just a continual force of Ffric = μk ·FN, pointing opposite whatever the current direction of movement is.

Static friction is a little different. It opposes the force on the object until it is overcome, at which point it switches to kinetic friction. It can cancel out other forces, but it never exceeds them.

MaximumStaticFriction = μs ·FN.

As usual, be careful when figuring out where all the forces go. A good free-body diagram goes a long, long way. And be extra careful when figuring out the normal force!

Friction

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

You have got enough understanding about mechanics, you will be able to understand how to use friction in our work.0024

First, let us get a sense of how friction works in two dimensions.0032

Imagine you have got a plank of wood that you are pushing along at a constant speed.0037

Here is some floor, here is some plank of wood on that floor, and we are pushing it along at a constant speed.0042

First thing to notice, is that in real life, we are used to the idea that if we want something to move, (since everything experiences friction), you have to push on it if you want to keep a constant speed.0047

It is not going to have that constant speed unless you push on it, because friction is going to sap the energy out of it.0057

So, for the first time, we are saying that we need a constant force to keep that constant speed.0064

Up until now, if we had any force at all, we would have had an acceleration automatically, because we have been talking about being on a frictionless surface.0071

It would be a small acceleration, but we would have had some acceleration because we would have had some force, unless all the forces are cancelling out.0079

Now, we are going to have all the forces cancel out, because we have friction cancelling out the forces we are putting in, so we can have a constant velocity.0086

With that out of the way, we have got this plank moving along at a constant speed, because we are putting in some force into it.0092

Now, which would be easier to push, which would take less push, which would take less force for pushing on the plank?0098

The plank was on a floor that is made of wood, or the plank on a floor made of rubber, which one of these will stick together more, which one will have more friction?0104

They behave differently with one another because of material science and chemistry and stuff that we are not going to really talk about, but friction is a pretty complicated idea that we will experience in lots of further courses and there is lots of cool interesting things to learn about it.0132

But in our case, we just know that, if we have different materials, we are going to have different frictions.0146

Different PAIRS of materials, that is an interesting thing to keep in mind, it is not just one material, it is the pair of it.0151

If we had a rubber plank on top of that rubber floor, we would have experienced even more friction.0157

An ice plank on top of an ice floor, it would have been the least of all.0161

That is because, this one has 'mg' down here, so it has got the pressure (the normal force) pushing that amount.0277

How much does this one on the right, how much is the force normal?0289

We have got 'mg' down here, but there is nothing this way, so our normal force, FN = 0, because there is no pressure, no interaction, nothing holding it against the wall to cause friction to happen.0293

If you push really hard on something, it is going to have more friction.0312

If you do not have any push between the things at all, there is no way for the materials to interact, there is no friction between them.0315

If we have a lot of normal force, if we push really hard on it, we are going to have more friction.0324

If we were to instead, come along and push crazy hard on this, then we are going to have a resultant normal force that is equal and opposite, we are going to have this normal force because it is not going to blow through that wall, assuming the wall is able to withstand that much force, we might actually to able to arrest the power of gravity, arrest the acceleration due to gravity, the force due to gravity will be canceled out because we will be able to make a really large friction by pushing really hard.0329

If you were to put the book up against the wall, and push really hard with the flat of your hand, not under it, because then you would be holding it up, it would not be friction, it would be just direct force applied through your finger tips.0370

But instead, if you were to push really hard against it, you will be able to keep it in place, because you put so much pressure on it, the friction of the book against the wall is going to be able to overcome the pull of gravity.0380

It is going to beat out gravity, and it is just going to stay still.0392

Just like you would expect, from all this talking, friction is not just weight, it is about how hard the object is pushed, it is about the pressure between the object and the surface, the two materials, the interaction, it is the normal force.0397

For those of you having trouble with calculating the normal forces on inclines, I would recommend you to refer to the 'Newton's second law in multiple dimensions lecture', it will give a good explanation.0410

You need to calculate just how much of the gravity is perpendicular and parallel to the surface.0429

To sum up, friction is based on the interaction between the materials involved in it, and the normal force of the object on the surface.0445

What kind of materials do we have, how hard the pressure is, the two things, the normal force.0451

If you want to turn that into an equation, that's going to become the friction = μ × FN...0458

μ is a Greek letter, and it is the coefficient of friction between the two materials, and it is spelled 'm-u', it will change depending on what the materials are, and it is going to vary a lot depending on specifics, and we have to determine it experimentally.0471

There is no easy formula for determining what it is going to be. You just have to go into a lab, get it, or look it up in a table.0493

Even in looking up a table, it is going to vary, because depending on the specific condition of the object, whether it is dirty, clean, if it is wet, if it has grease on it, if there is a layer of air, if it is operating in vacuum -- what things are happening between it, it is going to vary a lot.0499

So, it is basically up to you to figure it out in a lab, or to be able to look it up in a table where it has some very, very similar situations to the way you are doing it.0515

That has to do with the way friction works, it is what is happening on a really microscopic thing.0577

If we have a lot of area, the pressure per square area, the force per square area, is going to wind up being much smaller in the case when we have got that large surface.0583

So, same pressure, but it is going to be extended over a large area, whereas in the table example, where we have got just the little weak contacting, it is going to be the same pressure, but it is going to be over a small area, so the total effect is going to be the same, either a small force per area, but over large area, or a high force oer area, but over a small area, the total effect of the pressure is going to be the same.0600

So you do not have to worry about the cross-section, you just have to worry about the interaction between the materials.0628

Whatever direction it is moving in, keep in mind that it is the velocity , not the acceleration, whatever direction it is currently moving in, it is the opposite direction that the friction is going to point.0653

Friction always is fighting current motion, so the velocity, whatever the direction of velocity is, the opposite of that direction, is the direction that our friction is going to move in.0665

So with this point, we have got a pretty good understanding of how force works.0676

We have got, the block is the same in both diagrams, and the surface it is resting on is the same on both diagrams.0685

Let us assume that F1 and F2 are both big enough to move the block.0692

But also that, F1 and F2 are equal in magnitude, they are the same number of newtons.0696

If F1 and F2 have different orientations, but same magnitude, which block will accelerate faster?0707

If we break down our forces into components (we can do that since force is a vector), we look at the vertical amount in F1 and the horizontal amount in F1, and over here, the vertical amount of F2, and the horizontal amount of F2.0714

We see that the thing that is actually do the motion here, is this right here, it is going to be the actual horizontal motion is going to stem from the horizontal component of our force.0736

If we were instead looking at what the normal force is now, we need to figure out what the normal force is going to be.0752

So there is the force of gravity, and over here, it is going to be the exact same force of gravity, so force of gravity on both of them.0762

How much does the normal force has to be to cancel these things out.0769

Before when we were talking about the force of gravity and the normal force, they were going to be equal to one another (in the horizontal case), because the only thing creating the normal force is gravity.0774

But in this case, if you push through an object, and the object does not blow through the table, then that means that the table has to resist both the object's force of gravity, and in addition, the force that you put into the object.0789

So, the table, the surface has to resist both the forces, that has been put into it by ourselves, by the problem, and the force that is put into it by gravity.0803

In the first case on the left, it is going to have to fight both gravity, and the amount of the force, the normal force is going to be FN over here.0813

In this case, we have already got this component over here, is going to cancel out this component over here, so the normal force over here, is just going to be this little smidgen, down here.0825

In F2's case, we lift off some of the effective weight, what the normal force has to be is much smaller.0836

So which one of these is going to have a higher friction, this one is going to have a much smaller friction because it has got a much smaller normal force.0845

But over here, we have got this huge normal force in comparison, so we have got this giant friction.0862

We have got the same equal force horizontally, so we know that the giant friction is going to wind up sapping more of the acceleration and so, F2 is the more efficient, easier way, it is going to cause more acceleration.0866

F2 will accelerate the block faster, because it will have the smaller FN.0881

So it is really important to pay attention to the interaction between the force of gravity, then also the forces that we are putting into our object.0886

One more thing to talk about, is the idea of, an object being still, at rest on a surface, and an object moving along on a surface.0894

Just start a refrigerator moving, sliding on a floor, just start that refrigerator up, or keeping an already sliding refrigerator go away.0907

If we want to just, just start it moving up in addition to creating motion requiring some amount of force from us to get that started, there is actually going to be this little thing, if you have to sort of like, unstick it, we have to pop it off of where it was already located.0915

It might seem like a trick question, but it really is not, it really cannot take more force to start something moving than to just to fight kinetic friction.0932

That is a really complicated thing, it is something for future classes in chemistry, more physics, friction is something there is still doing lots of research into, so it is really complicated for right now, but it is definitely something interesting, but we do not have time to talk about it right now.0949

The exact reason is lots of complicated, but it suffices to say that on a microscopic level, the two surfaces interact differently between one another.0969

They are going to wind up interacting in a different way when they are going to be still, and when they are already moving against one another, slight differences happening microscopically , and sometimes major differences as we will see in some of the numbers that we are going to see soon.0976

Static versus kinetic, if we are going to be able to talk about two different kinds of friction, kinetic- the moving kind, and static- the still kind, we are going to have to use a different coefficient for each one.0993

So, μ is now going to split into two different categories: static is going to be μs, kinetic is going to be μk.1006

One thing to keep in mind: In almost all cases, μs is greater than μk,1020

There are a very few special cases where this is not going to be true, but as far as we are going to deal with in our course, it is almost always true, sometimes they will be equal and there is really freaky materials where μk is larger, but it is beyond this course, it is not something we are going to have to worry about.1029

If you get really interested in material science, it might be the kind of thing you have to deal with in graduate school, but not something that you have to worry about in high school physics.1052

If we have an object sitting still, and we push on that object, we have got an object like this, and it is giant, and a guy comes up, and he pushes on it, lightly.1080

It is going to be able to defeat him, but it is not going to go back with all of the friction, you know, if you have to push this lightly, if it is going to be able to cancel out this lightly, and this lightly, and say it is able to cancel out all the way up till this big, it is not going to react with the static friction force in the opposite direction of this big every time.1091

Static friction is going to be able to cancel out up to the amount of force, up to it is maximum amount.1113

So the maximum static friction, static friction resists an object starting to move it, until it gets surpassed.1119

Until we get to that really extreme case, we are always going to have the case that static friction is going to oppose however much force is put into it.1125

It is not going to put in more than that, it is just going to oppose the amount put into it, until we suddenly get to the point where we are able to equal and then surpass static, just that equal point is the razor's edge of flipping over into kinetic friction, at which point the object lurches forward, unsticks, starts to move, and then kinetic friction comes into play, and in almost always μk will be less than μs.1136

So we have some slight acceleration, if we kept up a constant force.1157

The static friction cancels out the force that would cause acceleration, but it never exceeds them.1160

That gives us, the maximum static friction = μs × FN, but keep in mind that it is the maximum static friction, not more than that, but just the maximum.1166

It is the top amount that it can be, we are not going to see that every time we put any small force into it, it is going to be the top amount, that is μs × FN.1179

These are some approximate values, this table here, keep in mind that these can vary depending on the specific situation, the condition of the materials involved, wet, greasy, air between them, perfect vacuum, there is certain material properties that can happen.1196

For the most part, these are going to remain the system, but it about the whole system interacting together, so it is really something that has to be experimentally determined, or given to us in the problem statement, or something we are solving for from the problem statement.1214

Take a look at these, these give us some idea how these things work.1226

Notice, μs and μk can change very greatly, the difference between cast iron when it is moving and when it is static, is vast, it is almost a tenth of what it start off as.1234

But rubber on concrete, it is not much of a change, it is still a change, but it is not giant.1248

Teflon on Teflon, Teflon starts off with a very low friction coefficient, but it stays the same whether it is moving or whether it is still, Teflon is the stuff that goes on to non-stick frying pans. (Teflon is actually a brand name, no one ever recognizes the chemical name, unless they learned it before in chemistry.)1258

This gives us some idea of what it is, we start to see that μs is almost always larger than μk, sometimes they are equal, and like I said before, there are few freaky cases where μk is larger.1277

It really can vary what it is, we see massive changes from 1.1 to 0.04, we can have even higher than 1.1, grip of a rock climbing shoes on rock is going to be even larger than 1.1, μk can get very small, μs can get very small, really depends on the situation.1301

You have to get it in the, either the problem statement, for most part we see numbers between 0.2 and 1 as the very highest, but for very slippery objects, we will see even lower, it has to do with what we are getting in the problem, and the specific materials we are working with in our case.1324

When the wheel is rolling, at the moment of contact, consider this sort of like flash forward thing, you have got some point here, and then that point is here, and then that point is here.1366

At the moment of contact, when it is right here, when it is on the ground, it is actually still because it gets laid down, and then it gets picked back up, it does not move relative to the ground until it is off of the ground.1382

If we have got this perfect circular wheel rolling, the wheel is not actually going to wind up having any friction on the ground.1396

In reality, the contact patch just moves slightly, but we are talking extremely small rolling resistance.1403

Notice, this does not mean that a car is being slowed by friction to the wheel.1425

Static friction can be very large, numbers like 1.0 for a wheel on concrete in dry conditions, but that does not mean that the car is taking all that out.1429

In fact, because it is being put down , and then it is moving off, it never moves, it is never trying to be moved around, when it is on ground, it is like it is practically still.1440

It is perfectly still from the point of view of the tyre at that moment.1452

That piece, that dot, does not start to move away until it is off of the ground.1455

Once it is off the ground, it can move around, because it is not going to have any friction.1459

So the only thing that creates friction is that tiny contact patch, and because that tiny contact patch is picked up before it moves relative to the earth, relative to the road, it is not going to give us any frictional force on our car.1463

So on the contrary, the fact that it is the static friction is what is going to allow the car to move smoothly, and experience practically no friction.1476

I have included bearings, and good oil, it being able to have a good wheel system, you are going to be able to have a almost frictionless motion, and you will be able to have all the motion to the car translated easily as it is running frictionless.1484

It is going to be way better than if we just had a metal body on the ground, that we are shoving along.1506

So, we will be able to experience effectively no friction, while it rolls along the ground in a straight line.1511

When the car turns, and tries to change its velocity, either by accelerating, so it is going to have those contact patches spinning up, because they are going to be moving faster than they were before, and this is a little complicated to think about.1516

But the acceleration, the force, it is the frictional force that allow the car to get that traction, which is why you sports cars, racing cars have really big flat large wheels, because they want a big contact patch, so they can get lots of force into the earth, where as cars that are trying for efficiency tend to have much thinner wheels.1530

If you want to be able to get a car that gets better fuel efficiency, you pump up the wheels a little bit heavier, because that will make them firmer, tighter, and will be able to have a less contact patch on the ground, which means they will have a little bit less friction.1553

Remember these are very small numbers, if you are driving at 100 miles, it can have an effect.1565

Or if you were to turn, that is when friction is going to come into play, normally you would have the wheel running like this, but then if we want to turn, the wheel is going to turn like this, but the motion of the car is going to be like this.1570

So, normally your wheels are going like this, and we have effectively no friction.1591

If instead we turn, the car has two choices, if it were to keep going in this path, then all of a sudden, friction will be breaking its contact patches with the earth, because that is not the direction wheel wants to roll in.1594

So, if the car were to keep going this way, it would break friction, friction would fight it.1612

So instead, it goes this way, which means that friction is going to wind up actually pulling this way.1618

This is a little bit complicated to think about, but the force of the wheels, friction is the only thing that connects the car to the earth.1622

The car and the road are connected through the friction of the tyres.1630

So when you go into a turn, the thing that pulls you into the turn, is going to be the friction of the wheels on the ground, and it is going to be μs.1634

This is a lot of explanation for something that does not seem to make sense, but if you want to be able to understand how a car rounds a corner, like we will in the section when we talk about uniform circular motion and force, we are going to be actually understand this.1641

So this stuff actually matters, it is a little complicated to think about at first, but it will make sense.1654

If something is going to be rolling, it effectively has, static friction, it effectively has no friction, because it is going to be putting in its contact patch, and lifting it up.1659

But if it wants to have an acceleration, that contact patch only has to move relative to the ground, otherwise, the rotation movement of the wheel is going to change the speed that the wheel is moving along.1667

So its going to require friction to be the interaction, the interplay between those two things.1678

Let us finally start talking about examples for the normal basic friction.1683

We have got a block of mass 10 kg, resting on a flat surface, horizontal force acting on it.1687

What angle θ will the block barely begin to slide, what is that instantaneous, that razor's edge, that break over point between staying still relative to the incline and suddenly starting to move along the incline?1912

Notice, for this problem, we do not have the mass of the block, but it turns it we are not actually going to need it.1920

So, we have got a block, it is going to weigh some 'm', so mg is the pull of gravity on it.1931

In this case, we get, F = 5 × mg, so the amount of force that we need to push it, to keep a constant velocity or keep it still (then we use μs) is going to be dependent on the coefficient of friction.2375

But, what about the fact that if they had different accelerations?2471

If they had different accelerations, then one of them is either going to be sliding off the other, or sliding behind the other, there is going to be a difference in their relative velocities, which means that they cannot be staying together anymore, they have to be slipping, by the definition of slipping.2477

That means, just to begin with, we know that the acceleration of the first block , has to equal the acceleration of the second block, so we can call them in general, 'a'.2494

We have got these 2 blocks, they are pulled along, only the bottom one is being pulled along, and the way it is able to communicate with the top one, the way that it is able to cause it to move, is by using friction.2568

The bottom one and the top one, they only communicate by friction, so friction has to be the way here.2579

If we are able to put so much force, this makes sense, I am sure you have seen it, if you have got 2 books on top of one another, we yank the bottom book really hard, the top book will just fall down, whereas if you yank the bottom book really slowly, they will both slide along easily together.2584

So it is going to be connected to the coefficient of friction, and the masses of the books.2598

What is going to be the minimum force to cause the top block to slip?2602

Now we could sub these things in, we could figure out what are the actual numbers, what also is friction.2807

In this case, friction = F / (1+2) = F/3, because that is the amount that it has to get, it is the share that the top block has to get, because it has one third the total mass of the system, so it has to get equal share for its mass, to be able to move it with the same acceleration.2813

So friction has to be equal to F/3, for the acceleration to be the same between both the objects.2841

Remember, that it is going to have maximum friction, (static friction, because we are static here), is going to be the maximum velocity without slipping.2849

Once again, it is that razor's edge, so the minimum velocity for slipping is going to be that flip over point, the maximum velocity without slipping is going to be the same thing as the minimum velocity of slipping, if we just go an infinitesimal amount over, we are going to start to slip.2863

So, the maximum static friction = the maximum velocity that we can move at.2886

ACTUALLY I SHOULD NOT HAVE SAID THE VELOCITY, THE MAXIMUM ACCELERATION, my apologies, you can of course have any velocity, it could be whizzing along in space, a million miles per hour, it does not matter.2894

From its point of view, it is not experiencing any force, so it is about the maximum acceleration.2906

That is how much it is, to finally get the thing to just start moving, if we just barely see 20.58, that is the razor's edge, slightest bit f difference off 20.58, and it will just start to slip, because it will just exceed this maximum static force.2976

Hope friction made sense, if you got difficulty in understanding how an incline works, definitely refer to Newton's second law in multiple dimensions, it will give you an understanding of how to deal with parallel and perpendicular forces, it is important to understand that when you are dealing with friction.2992

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